Kernel rig: construction cases, the plane through three points or vertices, and collinear points refused

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/kernel-cases/construction/cov-plane-three-points-on-vertices/expected.json

@@ -0,0 +1,22 @@
+{
+ "sources": [],
+ "what": "the plane through three vertices of a box",
+ "source": "analytic",
+ "method": "box 40 x 30 x 20 with a corner at the origin (x 0..40, y 0..30, z 0..20): vertices (40,0,0), (0,30,0), (0,0,20): x/40 + y/30 + z/20 = 1, normal (3,4,6)",
+ "construction": {
+  "T": {
+   "plane": {
+    "through": [
+     40,
+     0,
+     0
+    ],
+    "normal": [
+     3,
+     4,
+     6
+    ]
+   }
+  }
+ }
+}

tests/kernel-cases/construction/cov-plane-three-points-on-vertices/recipe.json

@@ -0,0 +1,40 @@
+{
+ "commands": [
+  {
+   "command": "solid.box",
+   "params": {
+    "length": 40,
+    "width": 30,
+    "height": 20,
+    "body_name": "Box"
+   }
+  },
+  {
+   "command": "construct.plane.three_points",
+   "params": {
+    "a": {
+     "vertex": [
+      40,
+      0,
+      0
+     ]
+    },
+    "b": {
+     "vertex": [
+      0,
+      30,
+      0
+     ]
+    },
+    "c": {
+     "vertex": [
+      0,
+      0,
+      20
+     ]
+    },
+    "name": "T"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-plane-three-points-refuses-collinear-points/expected.json

@@ -0,0 +1,8 @@
+{
+ "sources": [],
+ "what": "a plane through three points on one line",
+ "source": "analytic",
+ "method": "(0,0,0), (10,10,10), (20,20,20) are on one line: every plane through it holds them: refused",
+ "outcome": "refused",
+ "refusal": "the three points are on one line"
+}

tests/kernel-cases/construction/cov-plane-three-points-refuses-collinear-points/recipe.json

@@ -0,0 +1,31 @@
+{
+ "commands": [
+  {
+   "command": "construct.plane.three_points",
+   "params": {
+    "a": {
+     "point": [
+      0,
+      0,
+      0
+     ]
+    },
+    "b": {
+     "point": [
+      10,
+      10,
+      10
+     ]
+    },
+    "c": {
+     "point": [
+      20,
+      20,
+      20
+     ]
+    },
+    "name": "T"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-plane-three-points-slanted/expected.json

@@ -0,0 +1,22 @@
+{
+ "sources": [],
+ "what": "the plane through three box corners",
+ "source": "analytic",
+ "method": "(0,0,20), (40,0,20), (40,30,0): (40,0,0) x (40,30,-20) = (0,800,1200): normal (0,2,3) through (0,0,20)",
+ "construction": {
+  "T": {
+   "plane": {
+    "through": [
+     0,
+     30,
+     0
+    ],
+    "normal": [
+     0,
+     2,
+     3
+    ]
+   }
+  }
+ }
+}

tests/kernel-cases/construction/cov-plane-three-points-slanted/recipe.json

@@ -0,0 +1,31 @@
+{
+ "commands": [
+  {
+   "command": "construct.plane.three_points",
+   "params": {
+    "a": {
+     "point": [
+      0,
+      0,
+      20
+     ]
+    },
+    "b": {
+     "point": [
+      40,
+      0,
+      20
+     ]
+    },
+    "c": {
+     "point": [
+      40,
+      30,
+      0
+     ]
+    },
+    "name": "T"
+   }
+  }
+ ]
+}